Deterministic extinction by mixing in cyclically competing species

Emergence of vertical diversity under disturbance

We propose a statistical physics model of a neutral community, where each agent can represent identical plant species growing in the vertical direction with sunlight in the form of rich-get-richer competition. Disturbance added to this ecosystem, which makes an agent restart from the lowest growth level, is realized as a stochastic resetting. We show that in this model for sufficiently strong competition, vertical diversity characterized by a family of Hill numbers robustly emerges as a local maximum at intermediate disturbance.

Emergence and seismological implications of phase transition and universality in a system with interaction between thermal pressurization and dilatancy

A dynamic earthquake source process is modeled by assuming interaction among frictional heat, fluid pressure, and inelastic porosity. In particular, fluid pressure increase due to frictional heating (thermal pressurization effect) and fluid pressure decrease due to inelastic porosity increase (dilatancy effect) play important roles in this process. Two nullclines become exactly the same in the system of governing equations, which generates non-isolated fixed points in the phase space. These lead to a type of phase transition, which produces a universality described by the power law between the initial value of one variable and the final value of the other variable. The universal critical exponent is found to be 1/2, which is independent of the details of the porosity evolution law. We can regard the dynamic earthquake slip process as a phase transition by considering the final porosity or slip as the order parameter. Physical prediction of phase emergence is difficult because the porosity evolution law has uncertainties, and the final slip amount is difficult to predict because of the universality. Finally, nonlinear mathematical application of the result is also discussed.